I'm open to some kind of argument like "apple has no choice in such dictatorship" but this argument is contradictory with the argument that its protecting from nation states.
And since we mentioned Saudi arabia, we can also mention China where icloud is dodgy, it's not a unique case. I'm sure they are others I don't know about.
This is one service among all other government interactions services that the app provide. If the app is not here. Women still need to get male guardian approval because this is local law. You can disagree on that matter (I am not defending or debating it). I was just clarifying.
And yes, apple has to follow local laws. The app doesn't collect privacy invasive information used to track movements as your comment suggested. And it is not required to be on your phone.
While I usually don't like the saudi system but this app in particular is about making it easy to manage official government paperwork online [1]. This applies for all residents (citizens or not) and people really like it. So it is not an app to track females movements. While you can disagree or agree on the male approval requirements for a female to travel (I disagree) but it is not like it tracks movements using GPS or any invasive data. It just make it easier to manage the permits and all other interactions with the government without having to drive long distances and wait in lines.
Well as a complete outsider in another country who probably never went to Saudi Arabia like yourself, I would be more careful.
[1] https://en.wikipedia.org/wiki/Absher_(application)